1. Field of the Invention
This invention relates, generally, to ground penetrating radar. More specifically, it relates to the use of full-waveform inversion to better estimate the characteristics of underground objects and media.
2. Brief Description of the Prior Art
Modern life depends on subsurface pipelines used to carry water, oil, gas, sewage, and other fluids. Civil engineering and construction industries face the challenge of maintaining and repairing existing pipelines as well as laying new pipes. Increasing demand for new buried utilities increases the risk of damaging existing utilities (Lester and Bernold, 2007). As infrastructure ages, the demand for repairs and replacement requires knowledge of the locations and connectivity of multiple utility systems installed at different times, using different materials, in increasingly dense networks, in which records are often incomplete. In such scenarios, simply detecting a pipe at a given location may not be sufficient information. Ground-penetrating radar (GPR) resolution of not only the presence of the pipe, but also the pipe diameter, pipe material, or pipe-filling material (e.g., air, water, etc.) could be a way to distinguish and map different generations or types of utilities.
GPR has become one of the primary tools of choice for mapping the locations of pipes in urban settings. The transmitting antenna emits an electromagnetic (EM) pulse that propagates into the sub-surface. The EM pulse travels through the subsurface material, and it is reflected, scattered, and attenuated. The reflection or scattering occurs when the pulse encounters a subsurface inhomogeneity, in particular, soil heterogeneities or targets with contrasting dielectric properties (permittivity). Permittivity here is expressed as relative permittivity, which is the ratio of the material permittivity to the permittivity of free space. The pulse attenuation is primarily controlled by the electrical conductivity of the soil. Reflected energy is recorded by the receiving antenna. The signal recorded at the receiving antenna contains a combination of the energy traveling in air and along the ground surface, reflected and refracted energy from soil inhomogeneities, buried targets (in this case, pipes), and noise. A buried pipe generates a characteristic diffraction hyperbola because of its shape and contrast in EM properties with the background soil. The diffraction hyperbolas of pipes in GPR profiles are sufficiently distinctive such that they can be displayed and interpreted in real time; hence, GPR is widely used for on-the-spot utility detection.
The horizontal position of an underground pipe on a GPR profile is readily established as the location of the peak of the characteristic diffraction hyperbola (See FIG. 1). Inferring the depth to the top of the pipe requires knowledge of the average velocity structure of materials over the pipe. One way to derive the propagation velocity in the medium is by conducting a common-midpoint (CMP) or wide-angle reflection and refraction (WARR) survey, in which the spacing between the transmitter and receiver is progressively increased.
Following methods derived for stacking seismic data, layer velocities can be determined by semblance analysis (Fisher et al., 1992; Grandjean et al., 2000; Liu and Sato, 2014; Liu et al., 2014). This method has the advantage of recovering information on how velocity varies with depth, but it requires surveys with systems that permit a variable offset between transmitter and receiver. Alternatively, an average velocity can be determined from the shape and timing of the diffraction hyperbola that forms the GPR return from the pipe itself. So, in general, the pipe depth is estimated by finding the average velocity that best fits the measured hyperbola. However, Sham and Lai (2016) observe that the curve-fitting method is biased by human judgment.
The present invention focuses on how to extract additional information about pipes, beyond position and depth, from GPR profiles. The pipe diameter affects GPR returns, most visibly when the radar wavelength is small compared with the pipe diameter and the pipe's permittivity is significantly different from the surrounding soil (Roberts and Daniels, 1996). In this case, distinct returns can be captured from the top and bottom of the pipe, as shown in FIG. 1 (e.g., Zeng and McMechan, 1997). When the pipe is narrow enough that the top and bottom returns overlap and interfere, extracting information on pipe diameter from the single hyperbola is challenging. For example, Wiwatrojanagul et al. (2017) report no significant difference for the hyperbolic reflections for different rebar diameters. Diameter estimation based on fitting hyperbolas is clearly impacted by decisions about the phase of the pipe return selected for the fit (because one can choose either positive or negative phases; see Dou et al., 2017) and trade-offs made in wave velocity and pipe diameter selections. The hyperbola-fitting method also fails to provide any information about the pipe-filling material.
Ristic et al. (2009) present a method to estimate the radius of a cylindrical object and the wave propagation velocity from GPR data simultaneously based on the hyperbola fitting. In their method, the target radius is estimated by extracting the location of the apex of the hyperbola and the soil velocity that best fits the data for a point reflector, followed by finding an optimal soil velocity and target radius, using a nonlinear least-squares fitting procedure. This method is handicapped because the variability in the GPR source wavelet (SW) and local complexities in the soil's permittivity and conductivity structure affect the shape of the returned pulse. This in turn affects how the arrival times of diffracted returns are defined. These perturbations to the arrival time can be on the order of the changes expected with the changing cylinder diameter, making it difficult to distinguish the pipe diameter from the wavelet from the permittivity and conductivity complexities.
Other researchers have also investigated the complexities associated with pipe returns. For example, GPR can be applied for leakage detection from the pipes. Crocco et al. (2009) and Demirci et al. (2012) successfully detect water leakage from plastic pipes using GPR by applying microwave tomographic inversion and a back-projection algorithm, respectively. Ni et al. (2010) use a discrete wavelet transform (DWT) to filter and enhance GPR raw data to improve image quality. They find DWT to be advantageous in the detection of deeper pipes if shallower anomalies obscure the reflected signal from deeper targets, but they do not extract pipe diameter information. Janning et al. (2014) present an approach for hyperbola recognition and pipe localization in radargrams, which use an iterative-directed shape-based clustering algorithm to recognize hyperbolas and identify groups of hyperbola reflections that belong to a single buried pipe.
An alternative approach, upon which this invention relies, is full-waveform inversion (FWI) for selected properties of the subsurface. FWI uses information from the entire waveform. Virieux and Operto (2009) provide an overview of the development of using FWI for seismic data, but seismic wavelengths are typically too long to be useful for imaging subsurface utilities. FWI on GPR data is most commonly applied on crosshole GPR data to study aquifer material (e.g., Ernst et al., 2007; Klotzsche et al., 2010, 2012, 2013, 2014; Meles et al., 2010, 2012; Yang et al., 2013; Gueting et al., 2015, 2017; van der Kruk et al., 2015; Keskinen et al., 2017) or on frequency-domain air-launched GPR signals for a limited number of model parameters (Lambot et al., 2004; Tran et al., 2014; Andréet al., 2015; De Coster et al., 2016; Mahmoudzadeh Ardakani et al., 2016). Lavoué et al. (2014) use frequency domain FWI to image 2D subsurface electrical structures on multi-offset GPR data. Kalogeropoulos et al. (2011) use FWI on surface GPR data to monitor chloride and moisture content in media. Busch et al. (2012, 2014) apply FWI on surface GPR data to characterize soil structure and to obtain conductivity and permittivity estimations. Busch et al. (2013) further apply FWI on surface GPR data to estimate hydraulic properties of a layered subsurface.
While some of the studies above consider the combination of GPR data and FWI, none have applied ground surface GPR data for underground utilities or rebar in combination with FWI to provide improved resolution of utility/rebar dimensions and properties, compared to traditional GPR data analysis. Ground surface GPR surveys and the corresponding full waveform data from buried pipes/rebar can be inverted to achieve more accurate estimations of the depth, size, and infilling material of underground pipes/rebar than can be achieved with other methods described. However, in view of the art considered as a whole at the time the present invention was made, it was not obvious to those of ordinary skill in the field of this invention how the shortcomings of the prior art could be overcome.
All referenced publications are incorporated herein by reference in their entirety. Furthermore, where a definition or use of a term in a reference, which is incorporated by reference herein, is inconsistent or contrary to the definition of that term provided herein, the definition of that term provided herein applies and the definition of that term in the reference does not apply.
While certain aspects of conventional technologies have been discussed to facilitate disclosure of the invention, Applicants in no way disclaim these technical aspects, and it is contemplated that the claimed invention may encompass one or more of the conventional technical aspects discussed herein.
The present invention may address one or more of the problems and deficiencies of the prior art discussed above. However, it is contemplated that the invention may prove useful in addressing other problems and deficiencies in a number of technical areas. Therefore, the claimed invention should not necessarily be construed as limited to addressing any of the particular problems or deficiencies discussed herein.
In this specification, where a document, act or item of knowledge is referred to or discussed, this reference or discussion is not an admission that the document, act or item of knowledge or any combination thereof was at the priority date, publicly available, known to the public, part of common general knowledge, or otherwise constitutes prior art under the applicable statutory provisions; or is known to be relevant to an attempt to solve any problem with which this specification is concerned.